MacWilliams Identities for Rank metric codes over Galois rings

Abstract

The purpose of this paper is to study rank metric codes over Galois rings. In particular, we prove MacWilliams identities for finite chain rings relating the sequences of $q$-binomial moments of a code and its dual and for Gabidulin analogues of free codes over Galois rings we prove the corresponding MacWilliams identity as a functional expression relating the weight enumerator of the dual with the MacWilliams transform of the weight enumerator of the original code plus one extra term attached to the zero divisors.